The Wyoming Legislature consists of a Senate and a House of Representatives. The State Constitution provides that each of the State's 23 counties shall constitute a senatorial and representative district and shall have at least one senator and one representative, and requires the senators and representatives to be apportioned among the counties "as nearly as may be according to the number of their inhabitants." A 1981 Wyoming statute reapportioned the House of Representatives. Based on the 1980 census placing Wyoming's population at 469,557, the ideal apportionment would have been 7,337 persons per representative. But the reapportionment resulted in an average deviation from population equality of 16% and a maximum deviation of 89%. Niobrara County, the State's least populous county, was given one representative, even though its population was only 2,924, the legislature having provided that a county would have a representative even if the statutory formula rounded the county's population to zero. The legislature also provided that if Niobrara County's representation were held unconstitutional, it would be combined with a neighboring county in a single district so that the House would consist of 63 representatives. Appellants (members of the League of Women Voters and residents of seven counties in which the population per representative is greater than the state average) filed an action in Federal District Court, alleging that granting Niobrara County a representative diluted the voting privileges of appellants and other voters similarly situated in violation of the Fourteenth Amendment, and seeking declaratory and injunctive relief. The District Court upheld the constitutionality of the reapportionment statute.

Held: Wyoming has not violated the Equal Protection Clause of the Fourteenth Amendment by permitting Niobrara County to have its own representative. Pp. 842-848.

(a) Some deviations from population equality may be necessary to permit the States to pursue other legitimate objectives such as "maintaining the integrity of various political subdivisions" and "providing for compact districts of contiguous territory." Reynolds v. Sims,
377 U.S. 533, 578, 84 S.Ct. 1362, 1390, 12 L.Ed.2d 506. But an apportionment plan with population disparities larger than 10% creates a prima facie case of discrimination and therefore must be justified by the State, the ultimate inquiry being whether the plan may reasonably be said to advance a rational state policy and, if so, whether the population disparities resulting from the plan exceed constitutional limits. Pp. 842-843.

(b) This case presents an unusually strong example of an apportionment plan the population variations of which are entirely the result of the consistent and nondiscriminatory application of a legitimate state policy. Wyoming, since statehood, has followed a constitutional policy of using counties as representative districts and ensuring that each county has one representative. Moreover, Wyoming has applied the factor of preserving political subdivisions free from any taint of arbitrariness or discrimination. Pp. 843-846.

(c) Wyoming's policy of preserving county boundaries justifies the additional deviations from population equality resulting from the provision of representation for Niobrara County. Considerable population variations would remain even if Niobrara County's representative were eliminated. Under the 63-member plan, the average deviation per representative would be 13% and the maximum deviation would be 66%. These statistics make it clear that the grant of a representative to Niobrara County is not a significant cause of the population deviations in Wyoming. Moreover, the differences between the two plans are justified on the basis of the above policy of preserving county boundaries. By enacting the 64-member plan, the State ensured that this policy applies nondiscriminatorily, whereas the effect of the 63-member plan would be to deprive Niobrara County voters of their own representative. Pp. 846-848.

The issue is whether the State of Wyoming violated the Equal Protection Clause by allocating one of the 64 seats in its House of Representatives to a county the population of which is considerably lower than the average population per state representative.

* Since Wyoming became a State in 1890, its legislature has consisted of a Senate and a House of Representatives. The State's Constitution provides that each of the State's counties "shall constitute a senatorial and representative district" and that "each county shall have at least one senator and one representative." The senators and representatives are required to be "apportioned among the said counties as nearly as may be according to the number of their inhabitants." Wyo. Const., Art. 3, § 3.1 The State has had 23 counties since 1922. Because the apportionment of the Wyoming House has been challenged three times in the past 20 years, some background is helpful.

In 1963 voters from the six most populous counties filed suit in the District Court for the District of Wyoming challenging the apportionment of the State's 25 senators and 61 representatives. The three-judge District Court held that the apportionment of the Senateone senator allocated to each of the State's 23 counties, with the two largest counties having two senatorsso far departed from the principle of population equality that it was unconstitutional. Schaefer v. Thomson, 240 F.Supp. 247, 251-252 (Wyo.1964), supplemented, 251 F.Supp. 450 (1965), aff'd sub nom. Harrison v. Schaefer,
383 U.S. 269, 86 S.Ct. 929, 15 L.Ed.2d 750 (1966).2 But the court upheld the apportionment of the state House of Representatives. The State's constitutional requirement that each county shall have at least one representative had produced deviations from population equality: the average deviation from the ideal number of residents per representative was 16%, while the maximum percentage deviation between largest and smallest number of residents per representative was 90%. See 1 App. Exhibits 16. The District Court held that these population disparities were justifiable as "the result of an honest attempt, based on legitimate considerations, to effectuate a rational and practical policy for the house of representatives under conditions as they exist in Wyoming." 240 F.Supp., at 251.

The 1971 reapportionment of the House was similar to that in 1963, with an average deviation of 15% and a maximum deviation of 86%. 1 App. Exhibits 18. Another constitutional challenge was brought in the District Court. The three-judge court again upheld the apportionment of the House, observing that only "five minimal adjustments" had been made since 1963, with three districts gaining a representative and two districts losing a representative because of population shifts. Thompson v. Thomson, 344 F.Supp. 1378, 1380 (Wyo.1972).

The present case is a challenge to Wyoming's 1981 statute reapportioning its House of Representatives in accordance with the requirements of Art. 3, § 3 of the state Constitution. Wyo.Stat. § 28-2-109 (Supp.1982).3 The 1980 census placed Wyoming's population at 469,557. The statute provided for 64 representatives, meaning that the ideal apportionment would be 7,337 persons per representative. Each county was given one representative, including the six counties the population of which fell below 7,337. The deviations from population equality were similar to those in prior decades, with an average deviation of 16% and a maximum deviation of 89%. See 1 App. Exhibits 19-20.

The issue in this case concerns only Niobrara County, the State's least populous county. Its population of 2,924 is less than half of the ideal district of 7,337. Accordingly, the general statutory formula would have dictated that its population for purposes of representation be rounded down to zero. See § 28-2-109(a)(ii). This would have deprived Niobrara County of its own representative for the first time since it became a county in 1913. The state legislature found, however, that "the opportunity for oppression of the people of this state or any of them is greater if any county is deprived a representative in the legislature than if each is guaranteed at least one (1) representative."4 It therefore followed the state Constitution's requirement and expressly provided that a county would receive a representative even if the statutory formula rounded the county's population to zero. § 28-2-109(a)(iii). Niobrara County thus was given one seat in a 64-seat House. The legislature also provided that if this representation for Niobrara County were held unconstitutional, it would be combined with a neighboring county in a single representative district. The House then would consist of 63 representatives. § 28-2-109(a)(iv).

Appellants, members of the state League of Women Voters and residents of seven counties in which the population per representative is greater than the state average, filed this lawsuit in the District Court for the District of Wyoming. They alleged that "by granting Niobrara County a representative to which it is not statutorily entitled, the voting privileges of Plaintiffs and other citizens and electors of Wyoming similarly situated have been improperly and illegally diluted in violation of the 14th Amendment. . . ." App. 3-4. They sought declaratory and injunctive relief that would prevent the State from giving a separate representative to Niobrara County, thus implementing the alternative plan calling for 63 representatives.

The three-judge District Court upheld the constitutionality of the statute. 536 F.Supp. 780 (1982). The court noted that the narrow issue presented was the alleged discriminatory effect of a single county's representative, and concluded, citing expert testimony, that "the 'dilution' of the plaintiffs' votes is de minimis when Niobrara County has its own representative." Id., at 783. The court also found that Wyoming's policy of granting a representative to each county was rational and, indeed, particularly well suited to the special needs of Wyoming. Id., at 784.5

In Reynolds v. Sims,
377 U.S. 533, 568, 84 S.Ct. 1362, 1385, 12 L.Ed.2d 506 (1964), the Court held that "the Equal Protection Clause requires that the seats in both houses of a bicameral state legislature m st be apportioned on a population basis." This holding requires only "that a State make an honest and good faith effort to construct districts . . . as nearly of equal population as is practicable," for "it is a practical impossibility to arrange legislative districts so that each one has an identical number of residents, or citizens, or voters."
Id., at 577, 84 S.Ct., at 1390. See Gaffney v. Cummings,
412 U.S. 735, 745-748, 93 S.Ct. 2321, 2327-2329, 37 L.Ed.2d 298 (1973) (describing various difficulties in measurement of population).

We have recognized that some deviations from population equality may be necessary to permit the States to pursue other legitimate objectives such as "maintaining the integrity of various political subdivisions" and "providing for compact districts of contiguous territory." Reynolds, supra,
377 U.S., at 578, 84 S.Ct., at 1390. As the Court stated in Gaffney, "an unrealistic overemphasis on raw population figures, a mere nose count in the districts, may submerge these other considerations and itself furnish a ready tool for ignoring factors that in day-to-day operation are important to an acceptable representation and apportionment arrangement."
412 U.S., at 749, 93 S.Ct., at 2329.

In view of these considerations, we have held that "minor deviations from mathematical equality among state legislative districts are insufficient to make out a prima facie case of invidious discrimination under the Fourteenth Amendment so as to require justification by the State."
Id., at 745, 93 S.Ct., at 2327. Our decisions have established, as a general matter, that an apportionment plan with a maximum population deviation under 10% falls within this category of minor deviations. See, e.g., Connor v. Finch,
431 U.S. 407, 418, 97 S.Ct. 1828, 1835, 52 L.Ed.2d 465 (1977); White v. Regester,
412 U.S. 755, 764, 93 S.Ct. 2332, 2338, 37 L.Ed.2d 314 (1973). A plan with larger disparities in population, however, creates a prima facie case of discrimination and therefore must be justified by the State. See Swann v. Adams,
385 U.S. 440, 444, 87 S.Ct. 569, 572, 17 L.Ed.2d 501 (1967) ("De minimis deviations are unavoidable, but variations of 30% among senate districts and 40% among house districts can hardly be deemed de minimis and none of our cases suggests that differences of this magnitude will be accepted, without a satisfactory explanation grounded on acceptable state policy.") The ultimate inquiry, therefore, is whether the legislature's plan "may reasonably be said to advance a rational state policy" and, if so, "whether the population disparities among the districts that have resulted from the pursuit of this plan exceed constitutional limits." Mahan v. Howell,
410 U.S. 315, 328, 93 S.Ct. 979, 987, 35 L.Ed.2d 320 (1973).

B

In this case there is no question that Niobrara County's deviation from population equality60% below the meanis more than minor. There also can be no question that Wyoming's constitutional policyfollowed since statehoodof using counties as representative districts and ensuring that each county has one representative is supported by substantial and legitimate state concerns. In Abate v. Mundt,
403 U.S. 182, 185, 91 S.Ct. 1904, 1906-1907, 29 L.Ed.2d 399 (1971), the Court held that "a desire to preserve the integrity of political subdivisions may justify an apportionment plan which departs from numerical equality." See Mahan v. Howell, supra,
410 U.S. at 329, 93 S.Ct., at 987. Indeed, the Court in Reynolds v. Sims, supra, singled out preservation of political subdivisions as a clearly legitimate policy. See
377 U.S., at 580-581, 84 S.Ct., at 1391-1392.

Moreover, it is undisputed that Wyoming has applied this factor in a manner "free from any taint of arbitrariness or discrimination." Roman v. Sincock,
377 U.S. 695, 710, 84 S.Ct. 1449, 1458, 12 L.Ed.2d 620 (1964). The State's policy of preserving county boundaries is based on the state Constitution, has been followed for decades, and has been applied consistently throughout the State. As the District Court found, this policy has particular force given the peculiar size and population of the State and the nature of its governmental structure. See n. 5, supra; 536 F.Supp., at 784. In addition, population equality is the sole other criterion used, and the State's apportionment formula ensures that population deviations are no greater than necessary to preserve counties as representative districts. See Mahan v. Howell, supra,
410 U.S., at 326, 93 S.Ct., at 986 (evidence is clear that the plan " 'produces the minimum deviation above and below the norm, keeping intact political boundaries' "). Finally, there is no evidence of "a built-in bias tending to favor particular political interests or geographic areas." Abate v. Mundt, supra,
403 U.S., at 187, 91 S.Ct., at 1907-1908. As Judge Doyle stated below,

"there is not the slightest sign of any group of people being discriminated against here. There is no indication that the larger cities or towns are being discriminated against; on the contrary, Cheyenne, Laramie, Casper, Sheridan, are not shown to have suffered in the slightest degree. There has been no preference for the cattle-raising or agricultural areas as such." 536 F.Supp., at 788 (Doyle, J., specially concurring).

In short, this case presents an unusually strong example of an apportionment plan the population variations of which are entirely the result of the consistent and nondiscriminatory application of a legitimate state policy.6 This does not mean that population deviations of any magnitude necessarily are acceptable. Even a neutral and consistently applied criterion such as use of counties as representative districts can frustrate Reynolds' mandate of fair and effective representation if the population disparities are excessively high.7 "A State's policy urged in justification of disparity in district population, however rational, cannot constitutionally be permitted to emasculate the goal of substantial equality." Mahan v. Howell, supra,
410 U.S., at 326, 93 S.Ct., at 986. It remains true, however, as the Court in Reynolds noted, that consideration must be given "to the character as well as the degree of deviations from a strict population basis."
377 U.S., at 581, 84 S.Ct., at 1392. The consistency of application and the neutrality of effect of the nonpopulation criteria must be considered along with the size of the population disparities in determining whether a state legislative apportionment plan contravenes the Equal Protection Clause.

C

Here we are not required to decide whether Wyoming's nondiscriminatory adherence to county boundaries justifies the population deviations that exist throughout Wyoming's representative districts. Appellants deliberately have limited their challenge to the alleged dilution of their voting power resulting from the one representative given to Niobrara County.8 The issue therefore is not whether a 16% average deviation and an 89% maximum deviation, considering the state apportionment plan as a whole, are constitutionally permissible. Rather, the issue is whether Wyoming's policy of preserving county boundaries justifies the additional deviations from population equality resulting from the provision of representation to Niobrara County.9

It scarcely can be denied that in terms of actual effect on appellants' voting power, it matters little whether the 63-member r 64-member House is used. The District Court noted, for example, that the seven counties in which appellants reside will elect 28 representatives under either plan. The only difference, therefore, is whether they elect 43.75% of the legislature (28 of 64 members) or 44.44% of the legislature (28 of 63 members). 536 F.Supp., at 783.10 The District Court aptly described this difference as "de minimis." Ibid.

We do not suggest that a State is free to create and allocate an additional representative seat in any way it chooses simply because that additional seat will have little or no effect on the remainder of the State's voters. The allocation of a representative to a particular political subdivision still may violate the Equal Protection Clause if it greatly exceeds the population variations existing in the rest of the State and if the State provides no legitimate justifications for the creation of that seat. Here, however, considerable population variations will remain even if Niobrara County's representative is eliminated. Under the 63-member plan, the average deviation per representative would be 13% and the maximum deviation would be 66%. See 1 App. Exhibits 22. These statistics make clear that the grant of a representative to Niobrara County is not a significant cause of the population deviations that exist in Wyoming.

Moreover, we believe that the differences between the two plans are justified on the basis of Wyoming's longstanding and legitimate policy of preserving county boundaries. See
supra, at 841, n. 5, and 2696 - 2697. Particularly where there is no "taint of arbitrariness or discrimination," Roman v. Sincock,
377 U.S., at 710, 84 S.Ct., at 1458, substantial deference is to be accorded the political decisions of the people of a State acting through their elected representatives. Here it is noteworthy that by enacting the 64-member plan the State ensured that its policy of preserving county boundaries applies nondiscriminatorily. The effect of the 63-member plan would be to deprive the voters of Niobrara County of their own representative, even though the remainder of the House of Representatives would be constituted so as to facilitate representation of the interests of each county. See 536 F.Supp., at 784; id., at 786 (Doyle, J., specially concurring). In these circumstances, we are not persuaded that Wyoming has violated the Fourteenth Amendment by permitting Niobrara County to have its own representative.

By its decisions today in this case and in Karcher v. Daggett, --- U.S. ----,
103 S.Ct. 2653, 75 L.Ed.2d ---, the Court upholds, in the former, the allocation of one representative to a county in a state legislative plan with an 89% maximum deviation from population equality and strikes down, in the latter, a congressional reapportionment plan for the State of New Jersey where the maximum deviation is 0.6984%. As a member of the majority in both cases, I feel compelled to explain the reasons for my joinder in these apparently divergent decisions.

In my view, the "one-person, one-vote" principle is the guiding ideal in evaluating both congressional and legislative redistricting schemes. In both situations, however, ensuring equal representation is not simply a matter of numbers. There must be flexibility in assessing the size of the deviation against the importance, consistency, and neutrality of the state policies alleged to require the population disparities.

Both opinions recognize this need for flexibility in examining the asserted state policies.1 In Karcher, New Jersey has not demonstrated that the population variances in congressional districts were necessary to preserve minority voting strengththe only justification offered by the State. Id., --- U.S., at ----, 103 S.Ct., at 2665. Here, by contrast, there can be no doubt that the population deviation resulting from the provision of one representative to Niobrara County is the product of the consistent and nondiscriminatory application of Wyoming's longstanding policy of preserving county boundaries.

In addition, as the Court emphasizes, in this case we are not required to decide whether, and do not suggest that, "Wyoming's nondiscriminatory adherence to county boundaries justifies the population deviations that exist throughout Wyoming's representative districts." Ante, at 846. Thus, the relevant percentage in this case is not the 89% maximum deviation when the State of Wyoming is viewed as a whole, but the additional deviation from equality produced by the allocation of one representative to Niobrara County. Id., .

In this regard, I would emphasize a point acknowledged by the majority. See ante, at 2697. Although the maximum deviation figure is not the controlling element in an apportionment challenge, even the consistent and nondiscriminatory application of a legitimate state policy cannot justify substantial population deviations throughout the State where the effect would be to eviscerate the one-person, one-vote principle. In short, as the Court observes, ibid., there is clearly some outer limit to the magnitude of the deviation that is constitutionally permissible even in the face of the strongest justifications.

In the past, this Court has recognized that a state legislative apportionment scheme with a maximum population deviation exceeding 10% creates a prima facie case of discrimination. See, e.g., Connor v. Finch,
431 U.S. 407, 418, 97 S.Ct. 1828, 1835, 52 L.Ed.2d 465 (1977). Moreover, in Mahan v. Howell,
410 U.S. 315, 329, 93 S.Ct. 979, 987, 35 L.Ed.2d 320 (1973), we suggested that a 16.4% maximum deviation "may well approach tolerable limits."2 I have the gravest doubts that a statewide legislative plan with an 89% maximum deviation could survive constitutional scrutiny despite the presence of the State's strong interest in preserving county boundaries. I join the Court's opinion on the understanding that nothing in it suggests that this Court would uphold such a scheme.

The Court today upholds a reapportionment scheme for a state legislature featuring an 89% maximum deviation and a 16% average deviation from population equality. I cannot agree.

* Although I disagree with today's holding, it is worth stressing how extraordinarily narrow it is, and how empty of likely precedential value. The Court goes out of its way to make clear that because appellants have chosen to attack only one small feature of Wyoming's reapportionment scheme, the Court weighs only the marginal unequalizing effect of that one feature, and not the overall constitutionality of the entire scheme.
Ante, at 846, and nn. 8-9; see ante, at 849 (O'CONNOR, J., concurring). Hence, although in my view the Court reaches the wrong result in the case at hand, it is unlikely that any future plaintiffs challenging a state reapportionment scheme as unconstitutional will be so unwise as to limit their challenge to the scheme's single most objectionable feature. Whether this will be a good thing for the speed and cost of constitutional litigation remains to be seen. But at least plaintiffs henceforth will know better than to exercise moderation or restraint in mounting constitutional attacks on state apportionment statutes, lest they forfeit their small claim by omitting to assert a big one.

II

The Equal Protection Clause of the Fourteenth Amendment requires that a State, in apportioning its legislature, "make an honest and good faith effort to construct districts . . . as nearly of equal population as is practicable." Reynolds v. Sims,
377 U.S. 533, 577, 84 S.Ct. 1362, 1390, 12 L.Ed.2d 506 (1964). Under certain conditions the Constitution permits small deviations from absolute equality in state legislative districts,1 but we have carefully circumscribed the range of permissible deviations as to both degree and kind. What is required is "a faithful adherence to a plan of population-based representation, with such minor deviations only as may occur in recognizing certain factors that are free from any taint of arbitrariness or discrimination." Roman v. Sincock,
377 U.S. 695, 710, 84 S.Ct. 1449, 1458, 12 L.Ed.2d 620 (1964). "The overriding objective must be substantial equality of population among the various districts, so that the vote of any citizen is approximately equal in weight to that of any other citizen in the State." Reynolds,
377 U.S., at 579, 84 S.Ct., at 1390.

Our cases since Reynolds have clarified the structure of constitutional inquiry into state legislative apportionments, setting up what amounts to a four-step test. First, a plaintiff must show that the deviations at issue are sufficiently large to make out a prima facie case of discrimination. We have come to establish a rough threshold of 10% maximum deviation from equality (adding together the deviations from average district size of the most underrepresented and most overrepresented districts); below that level, deviations will ordinarily be considered de minimis. Ante, at 842-843; Connor v. Finch,
431 U.S. 407, 418, 97 S.Ct. 1828, 1835, 52 L.Ed.2d 465 (1977); White v. Regester,
412 U.S. 755, 763-764, 93 S.Ct. 2332, 2338-2339, 37 L.Ed.2d 314 (1973). Second, a court must consider the quality of the reasons advanced by the State to explain the deviations. Acceptable reasons must be "legitimate considerations incident to the effectuation of a rational state policy," Reynolds,
377 U.S., at 579, 84 S.Ct., at 1391, and must be "free from any taint of arbitrariness or discrimination," Roman,
377 U.S., at 710, 84 S.Ct., at 1458. See Mahan v. Howell,
410 U.S. 315, 325-326, 93 S.Ct. 979, 985-986, 35 L.Ed.2d 320 (1973). Third, the State must show that "the state policy urged . . . to justify the divergences . . . is, indeed, furthered by the plan,"
id., at 326, 93 S.Ct., at 986. This necessarily requires a showing that any deviations from equality are not significantly greater than is necessary to serve the State's asserted policy; if another plan could serve that policy substantially as well while providing smaller deviations from equality, it can hardly be said that the larger deviations advance the policy. See, e.g., Kilgarlin v. Hill,
386 U.S. 120, 123-124, 87 S.Ct. 820, 822-823, 17 L.Ed.2d 771 (1967); Mahan,
410 U.S., at 319-320, 326, 93 S.Ct., at 982-983, 986; Connor,
431 U.S., at 420-421, 97 S.Ct., at 1836-1837. Fourth, even if the State succeeds in showing that the deviations in its plan are justified by their furtherance of a rational state policy, the court must nevertheless consider whether they are small enough to be constitutionally tolerable. "For a State's policy urged in justification of disparity in district population, however rational, cannot constitutionally be permitted to emasculate the goal of substantial population equality." Mahan,
410 U.S., at 326, 93 S.Ct., at 986.

It takes little effort to show that Wyoming's 1981 House of Representatives apportionment is manifestly unconstitutional under the test established by our cases, whether one considers the instance of Niobrara County alone or in combination with the large deviations present in the rest of the scheme.

It is conceded all around, of course, that appellants have shown a prima facie case of discrimination. Wyoming's 89% maximum deviation greatly exceeds our "under 10%" threshold; indeed, so great is the inequality in this plan that even its 16% average deviation from ideal district size exceeds the threshold we have set for maximum deviations. On the other hand, one might reasonably concede that the State has met the second and third steps. Wyoming's long-standing policy of using counties as the basic units of representation is a rational one, found by the District Court to be untainted by arbitrariness or discrimination. It appears as well that the deviations at issue could not be reduced (at least not without substantially increasing the size of the House of Representatives) consistently with Wyoming's goals of using county lines and assuring each county at least one representative. It cannot plausibly be argued, however, that Wyoming's plan passes the fourth testthat its deviations, even if justified by state policy, be within the constitutionally tolerable range of size.

We have warned that although maintenance of county or other political boundaries can justify small deviations, it cannot be allowed to negate the fundamental principle of one person, one vote. E.g., Connor,
431 U.S., at 419, 97 S.Ct., at 1836. Likewise, we have recognized that it may not always be feasible, within constitutional constraints, to guarantee each county or subdivision a representative of its own. "Carried too far, a scheme of giving at least one seat in one house to each political subdivision (for example, to each county) could easily result, in many States, in a total subversion of the equalpopulation principle in that legislative body." Reynolds,
377 U.S., at 581, 84 S.Ct., at 1391 (footnote omitted); see Mahan,
410 U.S., at 349, n. 11, 93 S.Ct., at 997, n. 11 (BRENNAN, J., concurring in part and dissenting in part). And we have unambiguously rejected reliance on the very factor the State urges as the reason for its plan, stating that sparseness of population, far from excusing deviations from equality, actually increases the need for equality among districts:

"Sparseness of population is not a legitimate basis for a departure from the goal of equality. A State with a sparse population may face problems different from those faced by one with a concentrated population, but that, without more, does not permit a substantial deviation from the average. Indeed, in a State with a small population, each individual vote may be more important to the result of an election than in a highly populated State. Thus, particular emphasis should be placed on establishing districts with as exact population equality as possible." Chapman v. Meier,
420 U.S. 1, 24-25, 95 S.Ct. 751, 765, 42 L.Ed.2d 766 (1975) (emphasis added).

As the Court implicitly acknowledges,
ante, at 843, Niobrara County's overrepresentation60% compared to the ideal district sizecannot be considered "the kind of 'minor' variation which Reynolds v. Sims indicated might be justified by local policies counseling the maintenance of established political subdivisions in apportionment plans." Kilgarlin,
386 U.S., at 123, 87 S.Ct., at 822. In Kilgarlin, we expressed strong doubt that the 26% maximum deviation there could ever be permitted, ibid. In Mahan, we warned that a 16.4% maximum deviation, even though fully justified by state policy, "may well approach tolerable limits."
410 U.S., at 329, 93 S.Ct., at 987. See also Abate v. Mundt,
403 U.S. 182, 187, 91 S.Ct. 1904, 1907-1908, 29 L.Ed.2d 399 (1971). Here, by contrast, Niobrara County voters are given more than two and a half times the voting strength of the average Wyoming voter, and more than triple the voting strength of voters in some counties.2 "If a State should provide that the votes of citizens in one part of the State should be given two times, or five times, or 10 times the weight of votes of citizens in another part of the State, it could hardly be contended that the right to vote of those residing in the disfavored areas had not been effectively diluted." Reynolds,
377 U.S., at 562, 84 S.Ct., at 1381-1382. The creation of this district represents not a deviation from the principle of population equality, but an absolute disregard of it. Niobrara County, alone in the State, has been allocated a seat "on a basis wholly unrelated to population." WMCA, Inc. v. Lomenzo,
377 U.S. 633, 645, 84 S.Ct. 1418, 1424, 12 L.Ed.2d 568 (1964). This hardly constitutes "a faithful adherence to a plan of population-based representation." Roman,
377 U.S., at 710, 84 S.Ct., at 1458.

If the rest of the State is considered as well, the picture becomes even worse. The scheme's treatment of Niobrara County is not a single, isolated abuse, but merely the worst of many objectionable features. Of Wyoming's 23 counties, only nine are within as much as 10% of population proportionality. The populations per representative of Sublette and Crook Counties are, respectively, 38% and 28% below the statewide average; those of Washakie and Teton Counties are 29% and 28%, respectively, above that figure. The average deviation from ideal district size is 16%. The figures could be spun out further, but it is unnecessary. It is not surprising, then, that the Court makes no effort to uphold the plan as a whole. On the contrary, at least two Members of the majority express their "gravest doubts that a statewide legislative plan with an 89% maximum deviation could survive constitutiona scrutiny despite the State's strong interest in preserving county boundaries." Ante, at 850 (O'CONNOR, J., concurring).

C

The Court attempts to escape these stark facts through two lines of reasoning, each relying on an unspoken legal premise. Neither withstands examination.

First, the Court apparently assumes that the only aspect of unequal representation that matters is the degree of vote dilution suffered by any one individual voter. See ante, at 847. The Court is mistaken. Severe dilution of the votes of a relatively small number of voters is perhaps the most disturbing result that may attend invalid apportionments, because those unfortunate victims may be virtually disfranchised. It is not the sole evil to be combatted, however. It is equally illegal to enact a scheme under which a small group is greatly over -represented, at the expense of all other voters in the State. Such a "rotten borough"3 plan does tend to yield small figures supposedly measuring the harm to single individuals, as the Court's opinion illustrates; but that analysis overlooks the fact that very large numbers of persons are adversely affected.4 It is the principle of equal representation, as well as the votes of individual plaintiffs, that a State may not dilute. Reynolds,
377 U.S., at 578, 84 S.Ct., at 1390. Just as the Equal Protection Clause does not permit a small class of voters to be deprived of fair and equal voting power, so does it forbid the elevation of a small class of "supervoters" granted an extraordinarily powerful franchise. We would not permit Wyoming, in its legislative elections, to grant a double- or triple-counted vote to 2,924 voters because they were named Jones, or because they were licensed to practice laweven though such an enactment would, by the Court's reasoning, have only a de minimis effect on the rights of the rest of Wyoming's voters. Why, then, is it permissible to create such an exalted class based on location of residence?

The Court relies more directly on its unspoken assumption that we may judge the constitutionality of Niobrara County's representation by first severing that feature from the rest of the scheme, and then weighing it only by its incremental effect in increasing the degree of inequality present in the system as a whole.

"Appellants deliberately have limited their challenge to the alleged dilution of their voting power resulting from the one representative given to Niobrara County. The issue therefore is not whether a 16% average deviation and an 89% maximum deviation, considering the state apportionment plan as a whole, are constitutionally permissible. Rather, the issue is whether Wyoming's policy of preserving county boundaries justifies the additional deviations from population equality resulting from the provision of representation to Niobrara County." Ante, at 846 (footnotes omitted).

The first leg of this logicthat the Niobrara problem is legally severable from the rest of the planis contradicted by our prior decisions. The second legthat we should examine only the marginal unequalizing effectleads to exceptionally perverse results.

We confronted an analogous situation in Maryland Committee for Fair Representation v. Tawes,
377 U.S. 656, 84 S.Ct. 1429, 12 L.Ed.2d 595 (1964). The State argued in Tawes that since the plaintiffs had allegedly conceded that one house of the Maryland legislature was constitutionally apportioned, and the courts below had passed only on the apportionment of the other house, this Court was required to limit its consideration to the apportionment of the challenged house. We flatly rejected the argumen :

"Regardless of possible concessions made by the parties and the scope of the consideration of the courts below, in reviewing a state legislative reapportionment case this Court must of necessity consider the challenged scheme as a whole in determining whether the particular State's apportionment plan, in its entirety, meets federal constitutional requisites. It is simply impossible to decide upon the validity of the apportionment of one house of a bicameral legislature in the abstract, without also evaluating the actual scheme of representation employed with respect to the other house. Rather, the proper, and indeed indispensable, subject for judicial focus in a legislative apportionment controversy is the overall representation accorded to the State's voters, in both houses of a bicameral state legislature. We therefore reject the State's contention that the Court is precluded from considering the validity of the apportionment of the Maryland House of Delegates."
Id., at 673, 84 S.Ct., at 1438-1439.

Although we have not invariably adhered to this rule with regard to the two houses of a legislature, the concerns that led us in Tawes to examine both houses, despite the scope of the plaintiffs' complaint, forbid us to consider the allocation of one seat without also examining the remainder of Wyoming's apportionment of its House of Representatives. A plan with only a single deviationa good deal smaller than this one, and necessary to carry out a rational state policymight well be tolerated, even though in the same situation a greater number of substantial deviations would be unacceptable as too much of a departure from the goal of equality. See Lucas,
377 U.S., at 735, n. 27, 84 S.Ct., at 1473, n. 27. Where that greater number of deviations is present, as in this case, common sense as well as Tawes and Lucas require us to consider the plan as a whole. The inequality created by Niobrara County's representationa 23% increase in the maximum deviation from equalityis necessarily cumulative with the inequality imposed in the rest of the system. It is playing artificial tricks to assert that the fairness of the allocation of one seat in a legislative body can or should be considered as though it had no connection to the other seats, or to the fairness of their allocation. Indeed, the Court's own method contradicts its suggestion that the Niobrara problem is severable. The Court is fully willing to consider the system's other inequalities in this case, and even to give them controlling weightonly it wishes to consider those inequalities as weighing in favor of the plan. See infra, at this page and 860. I agree with the Court that we may not consider Niobrara County in a vacuum; it seems to me, however, that the existence of numerous instances of inequality ought to be considered an undesirable feature in an apportionment plan, n t a saving one. Only by examining the plan "in its totality," Lucas,
377 U.S., at 735, n. 27, 84 S.Ct., at 1473, n. 27, may we judge whether the allocation of any seat in the House is constitutional. This Court is not bound by a referendum of the League of Women Voters. See
ante, at 846, n. 8.

Here, Wyoming's error in granting Niobrara County voters a vote worth double or triple the votes of other Wyoming voters is compounded by the impermissibly large disparities in voting power existing in the rest of the apportionment plan. Supra, at 855. Yet, astonishingly, the Court manages to turn that damning fact to the State's favor:

"The allocation of a representative to a particular political subdivision still may violate the Equal Protection Clause if it greatly exceeds the population variations existing in the rest of the State and if the State provides no legitimate justifications for the creation of that seat. Here, however, considerable population variations will remain even if Niobrara County's representative is eliminated. . . . These statistics make clear that the grant of a representative to Niobrara County is not a significant cause of the population deviations that exist in Wyoming." Ante, at 847.

Under this reasoning, the further Wyoming's apportionment plan departs from substantial equality, the more likely it is to withstand constitutional attack. It is senseless to create a rule whereby a single instance of gross inequality is unconstitutional if it occurs in a plan otherwise letter-perfect, but constitutional if it occurs in a plan that, even without that feature, flagrantly violates the Constitution. That, however, is precisely what the Court does today.6

Justice O'CONNOR, joined by Justice STEVENS, states that she has "the gravest doubts that a statewide legislative plan with an 89% maximum deviation could survive constitutional scrutiny . . . ." Ante, at 850 (concurring opinion). But the Court today holds that just such a plan does survive constitutional scrutiny. I dissent.

"Each county shall constitute a senatorial and representative district; the senate and house of representatives shall be composed of members elected by the legal voters of the counties respectively, every two (2) years. They shall be apportioned among the said counties as nearly as may be according to the number of their inhabitants. Each county shall have at least one senator and one representative; but at no time shall the number of members of the house of representatives be less than twice nor greater than three times the number of members of the senate."

An example of the disparity in population was that Laramie County, the most populous county in the State, had two senators for its 60,149 people, whereas Teton County, the least populous county in the State, had one senator for its 3,062 people. See Schaefer v. Thomson, 240 F.Supp. 247, 250, n. 3 (Wyo.1964), supplemented, 251 F.Supp. 450 (1965), aff'd sub nom. Harrison v. Schaefer,
383 U.S. 269, 86 S.Ct. 929, 15 L.Ed.2d 750 (1966).

"(a) The ratios for the apportionment of senators and representatives are fixed as follows:

* * * * *

(ii) The ratio for the apportionment of the representatives is the smallest number of people per representative which when divided into the population in each representative district as shown by the official results of the 1980 federal decennial census with fractions rounded to the nearest whole number results in a house with sixty-three (63) representatives;

(iii) If the number of representatives for any county is rounded to zero (0) under the formula in paragraph (a)(ii) of this section, that county shall be given one (1) representative which is in addition to the sixty-three (63) representatives provided by paragraph (a)(ii) of this section;

(iv) If the provisions of paragraph (a)(iii) of this section are found to be unconstitutional or have an unconstitutional result, then Niobrara county shall be joined to Goshen county in a single representative district and the house of representatives shall be apportioned as provided by paragraph (a)(ii) of this section."

"It is hereby declared the policy of this state is to preserve the integrity of county boundaries as election districts for the house of representatives. The legislature has considered the present population, needs, and other characteristics of each county. The legislature finds that the needs of each county are unique and the interests of each county must be guaranteed a voice in the legislature. The legislature therefore, will utilize the provisions of article 3, section 3, of the Wyoming constitution as the determining standard in the reappo tionment of the Wyoming house of representatives which guarantees each county at least one (1) representative. The legislature finds that the opportunity for oppression of the people of this state or any of them is greater if any county is deprived a representative in the legislature than if each is guaranteed at least one (1) representative. The legislature finds that the dilution of the power of counties which join together in making these declarations is trivial when weighed against the need to maintain the integrity of county boundaries. The legislature also finds that it is not practical or necessary to increase the size of the legislature beyond the provisions of this act in order to meet its obligations to apportion in accordance with constitutional requirements consistent with this declaration." 1981 Wyo.Sess.Laws, ch. 76, § 3.

"Wyoming as a state is unique among her sister states. A small population is encompassed by a large area. Counties have always been a major form of government in the State. Each county has its own special economic and social needs. The needs of the people are different and distinctive. Given the fact that the representatives from the combined counties of Niobrara and Goshen would probably come from the larger county, i.e., Goshen, the interests of the people of Niobrara County would be virtually unprotected.

The people within each county have many interests in common such as public facilities, government administration, and work and personal problems. Under the facts of this action, to deny these people their own representative borders on abridging their right to be represented in the determination of their futures.

In Wyoming, the counties are the primary administrative agencies of the State government. It has historically been the policy of the State that counties remain in this position.

The taxing powers of counties are limited by the Constitution and some State statutes. Supplemental monies are distributed to the counties in accordance with appropriations designated by the State Legislature. It comes as no surprise that the financial requirements of each county are different. Without representation of their own in the State House of Representatives, the people of Niobrara County could well be forgotten." 536 F.Supp., at 784.

In contrast, many of our prior decisions invalidating state apportionment plans were based on the lack of proof that deviations from population equality were the result of a good-faith application of legitimate districting criteria. See, e.g., Chapman v. Meier,
420 U.S. 1, 25, 95 S.Ct. 751, 765, 42 L.Ed.2d 766 (1975) ("It is far from apparent that North Dakota policy currently requires or favors strict adherence to political lines. . . . Furthermore, a plan devised by [the special master] demonstrates that . . . the policy of maintaining township lines [does not] preven[t] attaining a significantly lower population variance."); Kilgarlin v. Hill,
386 U.S. 120, 124, 87 S.Ct. 820, 823, 17 L.Ed.2d 771 (1967) (per curiam ) (district court did not "demonstrate why or how respect for the integrity of county lines required the particular deviations" or "articulate any satisfactory grounds for rejecting at least two other plans presented to the court, which respected county lines but which produced substantially smaller deviations"); Swann v. Adams,
385 U.S. 440, 445-446, 87 S.Ct. 569, 572-573, 17 L.Ed.2d 501 (1967) (no evidence presented that would justify the population disparities).

"Carried too far, a scheme of giving at least one seat in one house to each political subdivision (for example, to each county) could easily result, in many States, in a total subversion of the equal-protection principle in that legislative body. This would be especially true in a State where the number of counties is large and many of them are sparsely populated, and the number of seats in the legislative body being apportioned does not significantly exceed the number of counties." Reynolds v. Sims,
377 U.S. 533, 581, 84 S.Ct. 1362, 1391-1392, 12 L.Ed.2d 506 (1964).

This discussion in Reynolds is illustrated by the senatorial districts in Wyoming that were invalidated in 1963. Each county in the State had one senator, while the two largest counties had two. Because county population varied substantially, extremely large disparities in population per senator resulted. The six most populous counties, with approximately 65% of the State's population, had eight senators, whereas the six least populous counties, with approximately 8% of the population, had six senators. See Schaefer v. Thomson, 240 F.Supp., at 251, n. 5. The Wyoming House of Representatives presents a different case because the number of representatives is substantially larger than the number of counties.

Counsel for appellants, who represent the state League of Women Voters, explained at oral argument that "a referendum had been passed by the League of Women Voters which authorized the attack of only that one portion of the reapportionment plan. It was felt by the membership or by the leadership of that group that no broader authority would ever be given because of the political ramifications and arguments that would be presented by the membership in attacking or considering . . . that broader authority." Tr. of Oral Arg. 8.

The dissent suggests that we are required to pass upon the constitutionality of the apportionment of the entire Wyoming House of Representatives. See post, at 857-859 (BRENNAN, J., dissenting). Although in some prior cases challenging the apportionment of one legislative house the Court has addressed the constitutionality of the other house's apportionment as well, we never have held that a court is required to do so. For example, in Gaffney v. Cummings,
412 U.S. 735, 93 S.Ct. 2321, 37 L.Ed.2d 298 (1973), we considered only the apportionment of the Connecticut General Assembly, noting expressly that the "Senate plan was not challenged in the District Court" and that "[a]ppellees do not challenge the Senate districts on the ground of their population deviations." Id., at 739, n. 5,
93 S.Ct., at 2324, n. 5. In this case, we see no reason why appellants should not be bound by the choices they made when filing this lawsuit.

Similarly, appellees note that under the 64-member plan, 46.65% of the State's voters theoretically could elect 51.56% of the representatives. Under the 63-member plan, 46.65% of the population could elect 50.79% of the representatives. See 1 App. Exhibits 32-33.

As the Court notes in this case, "consideration must be given 'to the character as well as the degree of deviations from a strict population basis.' . . . The consistency of application and the neutrality of effect of the nonpopulation criteria must be considered along with the size of the population disparities in determining whether a state legislative apportionment plan contravenes the Equal Protection Clause." Ante, at 845-846 (citation omitted). Similarly, in Karcher, the Court observes:

"The showing required to justify population deviations is flexible, depending on the size of the deviations, the importance of the State's interests, the consistency with which the plan as a whole reflects those interests, and the availability of alternatives that might substantially vindicate those interests yet approximate population equality more closely. By necessity, whether deviations are justified requires case-by-case attention to these factors." Id., --- U.S., at ----, 103 S.Ct., at 2663-2664.

The Court has recognized that States enjoy a somewhat greater degree of latitude as to population disparities in a state legislative apportionment scheme, which is tested under Equal Protection Clause standards, than in a congressional redistricting scheme, for which the Court has held that Art. I, § 2 of the Constitution provides the governing standard. White v. Regester,
412 U.S. 755, 763, 93 S.Ct. 2332, 2338, 37 L.Ed.2d 314 (1973).

The ideal district sizestatewide population divided by number of seatsis 7,337; Niobrara County's population is 2,924. Thus, the average representative represents 2.59 times as many constituents as Niobrara County's representative. Similarly, the populations of Washakie and Teton Counties are, respectively, 3.25 and 3.19 times as large as the population of Niobrara County, yet all three counties are given one representative each. 1 App. Exhibits 19-20.

"[In] Maryland Committee for Fair Representation v. Tawes, . . . we discussed the need for considering the apportionment of seats in both houses of a bicameral state legislature in evaluating the constitutionality of a state legislative apportionment scheme, regardless of what matters were raised by the parties and decided by the court below. Consistent with this approach, in determining whether a good faith effort to establish districts substantially equal in population has been made, a court must necessarily consider a State's legislative apportionment scheme as a whole. Only after evaluation of an apportionment scheme in its totality can a court determine whether there has been sufficient compliance with the requisites of the Equal Protection Clause."
377 U.S., at 735, n. 27, 84 S.Ct., at 1473, n. 27 (emphasis added). See also Burns v. Richardson,
384 U.S. 73, 83, 86 S.Ct. 1286, 1292, 16 L.Ed.2d 376 (1966).

This case also presents an issue as to what relief should be accorded. At an absolute minimum, the District Court should have granted the relief requested by appellantsthe combination of Niobrara and Goshen Counties into one district, as provided by the Wyoming legislature in case its first plan was found unconstitutional. See ante, at 840. That would have yielded a combined district of virtually perfect size, and would have reduced the plan's maximum deviation from 89% to 66%. This improvement alone23%is larger than any maximum deviation we have ever approved, with or without justification. See supra, at 854.

In my view, however, the District Court should have required Wyoming to devise an apportionment plan constitutional in its entirety. In Whitcomb v. Chavis,
403 U.S. 124, 91 S.Ct. 1858, 29 L.Ed.2d 363 (1971), the plaintiffs' complaint attacked Indiana's apportionment statute only as to one county. Id., at 137, 91 S.Ct., at 1865-1866. We reversed the District Court's judgment that that county was unconstitutionally apportioned. Nevertheless, we expressly approved the District Court's decision to expand the relief granted to include reapportionment of the entire State. "After determining that Marion County required reapportionment, the court concluded that 'it becomes clear beyond question that the evidence in this case and the additional apportionment requirements set forth by the Supreme Court call for a redistricting of the entire state as to both houses of the General Assembly.' " Id., at 161, 91 S.Ct., at 1878 (plurality opinion), quoting 305 F.Supp., at 1391; see
403 U.S., at 172-173, 179-180, 91 S.Ct., at 1884-1885, 1888-1889 (Douglas, J., concurring in the result in part). See also supra, at 857-859, and n. 5; Fed.Rule Civ.Proc. 54(c).